This invention relates to a method and apparatus for measuring wavefront sections of optical imaging systems and accomplishes this object without complex and expensive readout equipment. While directed specifically to measurement of wavefronts in the human eye, the invention is not limited in its application as an eye interferometer, since an additional object of the invention is its use as a fan trace interferometer for wavefront investigation of photographic objectives, reproduction lenses, telescopes, microscopes, enlarger lenses, and other imaging systems.
The human eye is an optical system characterized by aberrations of several types. One contributing factor to these aberrations is the fact that the human eye is not a rotationally symmetric optical system, because the fundus, where the vast majority of all vision takes place, is not located on the optical axis of the refracting elements of the eye, which optical axis makes an angle of 4.degree. to 7.degree. with the axis of best vision.
Due to the lack of coincidence of the optical axis with the axis of best vision of the eye lens system, leading to a rotationally asymmetric optical system with two perpendicular planes of symmetry, a large number of aberrations occur in the human eye optical system. The consequence of such aberrations is imperfect vision, ranging widely in degree of impairment of an individual's vision. So-called star rays, observed by most people to be emanating radially from a bright star at night, result from eye optical system aberrations,
Allviar Gullstrand was able to show mathematically that these star rays are due to aberrations caused by the optical system of the human eye. Helmholz also found that eyes without lenses, where the lenses have been removed due to cataracts, don't see these star rays.
Determination of aberrations of the type described require measurement of the phase of the light oscillation of a wavefront along the path of the wavefront where ray paths may be identified.
One crucial property of an interferometer is the provision to allow the measurement of the phase of the light oscillation of a wavefront. Because of the high frequency of the light oscillation, this measurement can only be achieved through comparison with a reference wave front of the same frequency. Another important property -- as far as an interferometer for the determination of lens aberrations is concerned -- relates to the fact that the phase measurement must be performed at a position along the path of the wavefront where ray paths may be identified. This allows it to trace the ray through the optical system and thus relate the phase measurement of the interferometer with a ray or a wavefront section which penetrates the aperture at a well defined location. For instance, if the phase measurement is performed at or near a caustic, it is not possible to determine the phase contributions of individual aperture sections, since the interferometer in this case measures the phase of the light oscillation which results from the vector addition of a large number of rays.
Therefore, whenever objects are "imaged" onto the retina, a ray convergence in the form of a caustic results. In fact, the size of the caustic is directly related to the aperture necessary to provide this resolution by the Helmholz-Lagrange formula, which may be interpreted as a sort of uncertainty relation: resolution size times aperture size is a constant; thus good resolution (small size) necessitates a large aperture.
Recent opthalmologic research indicates that cataracts introduce primarily phase errors in the various ray paths, while amplitude effects are not critically large. (Optical Engineering, "Holographic Phase Compensation Techniques Applied to Human Cataracts," Jan/Feb. 1973. ) Therefore, at least in principal, it is possible to compensate the phase errors of the cataract with an appropriate phase plate. Since holography cannot be applied to the in-vivo eye, these phase errors first have to be measured, and since it is absolutely necessary to assume a deviation from the spherical or toric shape of the wavefront, an instrument with interferometric resolution is required. On the other end of the scale, as shown by way of the star rays, even the resolution of the perfect eye could be improved, which would lead to improved night vision.
The inventive interferometer satisfies both interferometer requirements. It can be shown that there are only two rays intersecting at any point on the retina, and the interference of these two ray bundles generates a characteristic multi-stripe pattern which allows the phase measurement. Therefore, there is no caustic being generated on the retina, and no ambiguity about the origin of the phase error exists. Thus the inventive interferometer allows it to measure the vector contribution of all rays of a wavefront in the focal point where the caustic is normally formed. An important property of the eye interferometer is that a measurement in the eye can only be performed on the retina as the space between the retina and the eye lens is not accessible.
However, in testing camera lenses, for instance, a similar situation exists, in that the space between the film plane and the objective in many cameras is not accessible, and the inventive interferometer may be useful in those cases. However, if the situation requires a phase measurement outside the focal plane, the inventive interferometer works just as well.
Another important property of the interferometer is the complete absence of any phase ambiguity. It is well known that an interferometer which provides phase information in the form of a contour map of the wavefront has a serious phase ambiguity. While it is easily established that the phase differential between adjacent contour lines is 2 .pi., it is difficult to determine whether the phase is retarding or advancing in crossing from one line to the next. As the interferometer apparatus and method in the invention indicate, no such problem exists in the fan trace interferometer or its equivalent application, the eye interferometer.
Since corrective treatment first requires diagnostic measurement, one object of this invention is to measure phase errors of eye-optical defects, including mild cataracts to supply information needed to construct a suitable compensatory lens. In addition, the resolution of the perfect eye is capable of improvement after a proper measurement of eye aberrations by the invention.